Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes

In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not onlyapproximations of the values of a function at some missing points can be obtained, butalso uncertainty estimates for such predicted values. This random scheme generalizes theusual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero meanand given variance, and generating, in the limit, a Gaussian process whose correlationstructure is characterized and used for computing realizations of the conditional posteriordistribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many predictionpoints need to be considered